Usage of Syntax Directed Translation and DAG in Compiler Design

Yash Gaherwar

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Apr 16, 2023

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Authors:- Yash Gaherwar, Tanishq Deshpande, Devanshu Dalal, Avinash Dhakne

In this article we will be discussing regarding some of the most important topics in “Compiler Design” i.e. Syntax Directed Translation (SDT) and Directed Acyclic Graph (DAG). We will be discussing the usage of SDT and DAG in Compiler Design, about their applications, advantages, disadvantages and complexity analysis of DAG and Parse Tree.

What is Syntax Directed Translation?

As we are all aware, the Parser checks the input string for accuracy before producing output for the following stage of the compiler. A parse tree or an abstract syntax tree could be the output. Now we employ Syntax Directed Translation to sandwich semantic analysis between the compiler’s syntax analysis step.

Grammar rules that are enhanced by Syntax Directed Translation make it easier to perform semantic analysis. SDT entails feeding the parse tree data that is attached to the nodes as attributes from the bottom up or from the top down. The lexical values of nodes, constants, and characteristics related to non-terminals are all used in the formulations of syntax-directed translation rules.

Flow Diagram:-

Syntax-directed translation benefits include:

1. Implementation simplicity: SDT is a straightforward and simple method for translating a programming language. It offers a straightforward and organized way to define translation rules using grammatical rules.
2. Separation of concerns: SDT divides the parsing and translation processes, which makes it simpler to update and maintain the compiler. Additionally, it separates the problems about translation from the concerns about parsing, enabling more modular and adaptable compiler designs.
3. Effective code generation: SDT makes it possible to generate code that is effective by streamlining the translation procedure. It permits the application of strategies like intermediate code creation and code optimisation.

Syntax Directed Translation’s drawbacks:-

1. SDT’s expressiveness is constrained when compared to other translation techniques, like attribute grammars. The kinds of translations that can be carried out using SDT are so constrained.
2. SDT may be rigid in circumstances where the translation rules are complicated and difficult to express using simple grammatical principles.
3. Limited mistake recovery: The ability of SDT to correct translation errors is constrained. This may lead to subpar error messages and make it more challenging to find and correct input programme issues.

What is Directed Acyclic Graph?

A Directed Acyclic Graph (DAG) is a directed graph that contains nodes connected by edges, with the property that the graph contains no directed cycles. This means that it is impossible to start at any node and follow a sequence of edges that eventually loops back to the starting node.

The absence of cycles makes DAGs useful in a variety of applications, particularly in compiler design and optimization. For example, in a compiler, a DAG can be used to represent the control flow and data dependencies of a program, enabling the compiler to perform optimizations such as common sub-expression elimination and loop invariant code motion.

DAGs are also commonly used in scheduling problems, where the goal is to schedule a set of tasks subject to constraints such as precedence relations and resource availability. The tasks are represented as nodes in the DAG, with edges representing the precedence relations between tasks.

In addition, DAGs are used in a variety of other applications, such as in data processing pipelines, where each node in the graph represents a processing step and the edges represent the flow of data between steps.

Overall, the Directed Acyclic Graph is a powerful and versatile data structure that finds many applications in computer science and related fields.

Usage of DAG in Compiler Design:-

1. In compiler design, a Directed Acyclic Graph (DAG) is commonly used to represent the control flow and data dependencies of a program. This representation is often used as an intermediate representation (IR) that facilitates program optimization and transformation.
2. When a program is compiled, it goes through several stages, including lexical analysis, parsing, semantic analysis, and code generation. During these stages, the compiler constructs a DAG representation of the program that captures the control flow and data dependencies between its components.
3. One common use of DAGs in compiler design is to represent expressions. An expression can be represented as a DAG in which each node represents a sub-expression, and each edge represents a dependency between sub-expressions. The use of DAGs in this context enables the compiler to perform optimizations such as common sub-expression elimination and constant folding, which can significantly improve the performance of the generated code.
4. Another use of DAGs in compiler design is to represent the control flow of a program. A control flow DAG is a representation of the program’s control flow in which each node represents a basic block of code, and each edge represents a control flow transfer between basic blocks. Control flow DAGs can be used to perform optimizations such as dead code elimination and loop unrolling.
5. Overall, the use of DAGs in compiler design provides an efficient and effective approach to representing the control flow and data dependencies of a program, enabling the compiler to perform a variety of optimizations that can significantly improve the performance of the generated code.

Usage of Syntax Directed Translation (SDT) in Compiler Design:-

• Syntax Directed Translation (SDT) is a technique used in compiler design to define the translation of a programming language’s source code into machine code or some other intermediate representation. In SDT, translation rules are associated with the grammar productions of the language, and these rules are executed during the parsing process to produce the desired output.
• One of the main advantages of SDT is that it enables the compiler designer to specify the translation process in a declarative manner, which is much easier to understand and maintain than a procedural implementation. Additionally, SDT can enable certain optimizations, such as constant folding and common sub-expression elimination, by associating translation rules with particular productions in the grammar.
• The basic steps involved in using SDT in compiler design are as follows:

1) Define the grammar of the programming language.

2) Each grammatical production should be associated with a set of translation rules.

3) Use a parser generator to generate a parser for the language.

4) As the parser processes the input program, execute the translation rules associated with each production to produce the desired output.

• Overall, the use of Syntax Directed Translation in Compiler Design provides a powerful and flexible approach to defining the translation process for a programming language. By associating translation rules with the grammar productions, SDT enables the compiler to generate efficient and optimized code, while also making the translation process easier to understand and maintain.

Complexity Analysis of DAG in Compiler Analysis:-

• In compiler design, Directed Acyclic Graphs (DAGs) are often used to represent the control flow and data dependencies of a program, and they play a crucial role in optimizing the generated code. The complexity analysis of DAGs in compiler design depends on the specific optimization being performed.
• Here are some common optimizations that use DAGs and their associated time complexities:

1. Common Subexpression Elimination (CSE): O(n²)

→ CSE is an optimization that eliminates redundant computations by identifying common subexpressions in the program. The time complexity of CSE using DAGs is O(n²), where n is the number of nodes in the DAG.

2. Dead Code Elimination (DCE): O(n)

→ DCE is an optimization that eliminates code that is never executed. The time complexity of DCE using DAGs is O(n), where n is the number of nodes in the DAG.

3. Register Allocation: O(n³)

→ Register allocation is an optimization that assigns variables to hardware registers to minimize the number of memory accesses. The time complexity of register allocation using DAG is O(n³), where n is the number of nodes in the DAG.

4. Loop Optimization: O(n²)

→ Loop optimization is an optimization that optimizes the performance of loops in the program. The time complexity of loop optimization using DAGs is O(n²), where n is the number of nodes in the DAG.

• Overall, the time complexity of using DAGs in compiler design depends on the specific optimization being performed, but in general, it tends to be relatively efficient. Most optimizations take quadratic or cubic time in the size of the DAG, which is usually much smaller than the size of the original program.

Can Syntax Directed Translation be Performed using Parse Tree?

→ SDT can be performed using a parse tree or an abstract syntax tree (AST).

• The syntactic structure of source code is represented as a tree in a parse tree, where each node corresponds to a production in the grammar used to parse the input program. Parse trees are often used in bottom-up parsing techniques, such as LR parsing.

For Example:- Parse Tree Construction for => 2*(4+5)

1. In SDT using a parse tree, translation rules are associated with each production in the grammar, and these rules are executed during the parsing process to produce the desired output.
2. The translation rules are typically expressed as semantic actions associated with the grammar productions, which are executed when the corresponding production is reduced during parsing.
3. The main advantage of using a parse tree for SDT is that it provides a detailed representation of the syntactic structure of the input program, which makes it easier to perform context-sensitive analysis and generate accurate error messages.
4. However, parse trees tend to be more complex and memory-intensive than ASTs.

Can Syntax Directed Translation be Performed using Abstract Syntax Tree?

• In contrast, an abstract syntax tree (AST) is a simplified representation of the syntactic structure of the input program that only includes the essential information for performing the desired translation. ASTs are often used in top-down parsing techniques, such as recursive descent parsing.

For Example:- Abstract Syntax Tree Construction for => 2*(4+5)

1. In SDT using an AST, translation rules are associated with the nodes in the tree, and these rules are executed during a traversal of the tree to produce the desired output. The translation rules are typically expressed as methods or functions associated with the node types in the AST.
2. Overall, both parse trees and ASTs can be used for SDT in compiler design, and the choice of representation depends on the specific requirements of the compiler and the parsing technique being used.

Conclusion:-

From hereby we can conclude that Directed Acyclic Graphs (DAGs) and Syntax Directed Translation (SDT) are two essential techniques used in compiler design to optimize and translate source code into machine code or other intermediate representations. DAGs provide a powerful tool for representing the control flow and data dependencies of a program, which is critical for optimizing the generated code. Meanwhile, SDT allows for a straightforward and efficient translation process that associates semantic actions with the nodes in the parse tree or AST, allowing for accurate and efficient code generation. The combination of DAGs and SDT techniques in compiler design can lead to efficient, optimized, and reliable code generation, making them essential tools for modern compilers.

Hope this blog will be helpful in understanding the the core concept of compiler design i.e. Syntax Directed Translation and Directed Acyclic Graph.